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In this paper a remarkable simple proof of the Gauss’s generalization of the Wilson’s theorem is given. The proof is based on properties of a subgroup generated by element of order 2 of a finite abelian group. Some conditions equivalent to the cyclicity of (Φ(n), ·n), where n > 2 is an integer are presented, in particular, a condition for the existence of the unique element of order 2 in such a...
Some basic rules concerning the theory and the consequences of natural selection are presented and the definition of natural selection is given according to Endler (1986). The concept of fitness and its diverse definitions are presented and a short account of natural selection as the process of changes in gene frequencies is given. Some counterintuitive examples of the outcomes of selection and its...
This article is a short account of the theory of the genetic drift and some of its important consequences. In order to explain this theory simple simulation in Microsoft Excel is applied to show what one can expect in a large population divided into many small populations and some very basic formula concerning the genetic drift are introduced. These introductions allow the presentation of the fate...
This article shortly discusses why natural selection should be considered at the level of genes, instead of individuals. This standpoint is justified with kin selection theory, the concept of selfish gene and the conflicts within genomes. The reasons for the introduction of group selection are explained and the idea of the adaptation for the good of species is critically discussed. Two theoretical...
In this article the relations between heredity and the evolution by natural selection are discussed. The Darwin's attempts to solve the problems of heredity were based on pre-Mendelian intuitions, and the discovery of the Mendelian rules inclined some outstanding geneticists to reject the Darwinian theory of natural selection. The difficulties of combining genetics with the theory of natural selection...
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